Hexagon Atom circle wire frame
You can use Dupliverts.

Add a big icosphere and at its center, a small one.

Parent the small one to the big one. (select small, then big, Ctrl+P, Object)

Select the big sphere,go to Object panel, in Duplication, click Verts.

The little sphere is now replicated on every vertex of the big one. Notice that the faces of the big sphere won't be rendered, despite they appear in the 3D view.

Now you can duplicate the big sphere (Shift+D), disable duplications on it, and add a Wireframe modifier.